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## Bug in PolynomialIdeals

Maple 16

Hello,

I am experiencing wrong results using the PolynomialIdeals package in Maple 16 (see radical_error.mw). Creating the same ideal with different generators, the radicals computed differ which of course is wrong:

with(PolynomialIdeals);
J := <t*(a+A), A*(b+B+t), b*(a+A), B*a-A*(b+t), (variables = {A, B, a, b, t})>:
J2 := <t*(a+A), A*(b+B+t), b*(a+A), B*(a+A), (variables = {A, B, a, b, t})>:
IdealContainment(J2, J, J2);
IdealContainment(R, J);
IdealContainment(R2, J2);
true
false
true

So J and J2 are the same, but the radicals differ. In fact, the ideal is radical so R2=J2 is the correct result, while in the first case PolynomialIdeals gives a larger radical. It has the (wrong) additional generator p from

p := b*A*(b+B):
IdealMembership(p, R);
IdealMembership(p, R2);
true
false

Is there a quick way to fix this? Unfortunately I can not continue my work as I need a working (and correct) method to calculate the radicals.

Thank you very much,

Erik

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